The value of the algebraic expression is:
a^2*b = -15 + 20i
How to find the value of the expression?
Here we have the following expression:
a^2*b
And we want to use the values:
a = -1 + 2i
b = 5
Replacing these values in the expression we will get:
(-1 + 2i)^2*5
Expanding the first part we get:
(-1 + 2i)*(-1 + 2i) = (-1)*(-1) + (-1)*(2i) + (2i)*(-1) + (2i)*(2i)
= 1 - 2i - 2i - 4
= -3 + 4i
Replacing that in the expression we get:
(-1 + 2i)^2*5 = (-3 + 4i)*5 = -3*5 + 4i*5 = -15 + 20i
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An orange grove manager uses two different sized buckets to load oranges into a truck. The first bucket can transport a pound of oranges, and the second bucket can transport
y pounds of oranges. The first bucket is filled up G times and the second bucket is filled up I times The total amount of oranges. I that have been loaded can be found usina
the equation T = Ga + Hy.
Solve for H.
T + Ge
O H
y
O H= y(T - Gx)
T
0 H = Gx+y
T_ Cr
O H
2
On solving for [H], we get -
H = (T - Ga)/y
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the following equation -
T = Ga + Hy
We have -
T = Ga + Hy
Solving for [H], we get -
Hy = T - Ga
H = (T - Ga)/y
Therefore, On solving for [H], we get -
H = (T - Ga)/y
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How to solve 3-2/5x-12/5=10-2x/5
The graph below shows the relationship between the number of ounces and the number of calories in steak.
Which equation best represents this relationship?
Responses
Answer:
??
Step-by-step explanation:
where are the equations ?
Answer:
Step-by-step explanation:
-1/4-a-4=7/4a-3
solving equations with one unlike equations
Answer:
a = -5/11
Step-by-step explanation:
You want to solve the equation -1/4-a-4=7/4a-3.
SolutionThe first step in solving this 3-step equation can be to add the opposite of (-a) so that the variable 'a' appears only on one side of the equation:
-1/4 -a -4 +a = 7/4a -3 +a
-17/4 = 11/4a -3 . . . . . . . . . . . simplify
The second step is to add the opposite of the constant (-3) so that the constant is on one side of the equation, and the variable is on the other side.
-17/4 +3 = 11/4a -3 +3
-5/4 = 11/4a . . . . . . . . . . simplify
The third step is to multiply by the inverse of the coefficient of the variable:
(4/11)(-5/4) = (4/11)(11/4a)
-5/11 = a . . . . . . . . . . . . . . . simplify
Check-1/4 -(-5/11) -4 = (7/4)(-5/11) -3
-17/4 +5/11 = -35/44 -3
(-187 +20)/44 = (-132 -35)/44
-167/44 = -167/44 . . . . . . answer checks OK
Compute the probability of tossing a six sided die with sides numbered 1 through 6 and getting a 5
The probability of tossing a six-sided die with sides numbered 1 through 6 and getting a 5 is 0.166666 or 1/6.
Here in the question, we see that a six-sided die is tossed. So there will be a total of 6 outcomes.
So the sample space will be {1,2,3,4,5,6}
Of which the possible outcome of getting a 5 is 1
Let A be the event of getting a 5 on tossing a six-sided die
∴ the probability of getting a 5 on tossing a six-sided die is P(A)=1/6
∵ we know that the probability of an event is the possible outcome of the event divided by the total outcomes of that event.
So here the probability of getting a 5 is 0.166666 or 1/6.
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Write the prime factorization of 48
The prime factorization of 48 is 2⁴ × 3.
What are prime numbers?Those greater than one are known as prime numbers. They simply have two variables: the number itself and factor 1. This indicates that these numbers cannot be divided without leaving a remainder by any number other than 1 and the number itself.
Given:
The number is 48,
Factorize 48 we get 2 × 2 × 2 × 2 × 3
= 2⁴ × 3
Therefore, the prime factorization of 48 is 2⁴ × 3.
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Consider the function graphed at right.
The function has a maximum
of 3
The function is increasing on the interval(s):
The function is decreasing on the interval(s):
at x =
-4
4
-32
-5--
3 4 5
1 2 3 4 5
Answer:
heyyyyyyyyyyyyyyyyyyyyyyyy
What is the b-value?
Answer:
3
Step-by-step explanation:
y-intercept = b
The slope-intercept = y=mx+b
y=-2/5x+3
m=-2/5
b=3
If the equation was something like y=-2x-3, then the b would be -3 because you are subtracting 3.
In your own words, describe the y-intercept.
Answer:
The y-intercept is the point where the graph ( line or curve ) intercepts the y-axis. The y-intercept is the y value of the point, ( x, y ).
Hope this helps!
Step-by-step explanation:
HELP! Recursive and explicit growth problem
The populations, considering an exponential function, are given as follows:
P(1) = 19.2.P(2) = 23.04.P(12) = 142.66.What is an exponential function?An increasing exponential function is modeled according to the rule presented as follows:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which the variables of the function are:
A(0) is the initial amount of the function.r is the growth rate of the function, as a decimal.In this problem, the parameters are given as follows:
A(0) = 16, r = 0.2.
Hence the function, written as P(t), is:
[tex]P(t) = 16(1.2)^t[/tex]
The numeric values are found replacing the lone instance of t by the value at which we want to find the numeric value, hence:
P(1) = 16 x (1.2)¹ = 19.2.P(2) = 16 x (1.2)² = 23.04.P(12) = 16 x (1.2)¹² = 142.66.More can be learned about exponential functions at https://brainly.com/question/25537936
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what is 1311 divided by 20=?
using long division and with a remainder
The value of the solution of division is 115 with the remainder 11.
We have to give that,
1311 divided by 20.
Now, using long division as,
1311 divided by 20.
20 ) 2311 ( 115
- 20
------------
31
- 20
------
111
- 100
--------
11
Hence, the solution of division is, 115 with the remainder 11
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simplify this expression-12÷3×(-8+(-4)²-6)+2
Answer: -6
Step-by-step explanation:
write 10 forms for 1 over 8 as you can think of, be creative and use positive and negative powers or other forms of number.
Answer:
No entendí porfavor puedes ponerlo en Español
1. Use the picture to answer the following questions.
2. Find the missing value(s) in the ratio table.
The ratio of snakes to frogs is 1 : 2.
The ratio of frogs to animals is 2 : 3.
If 3 more snakes are added, the number of frogs that should be added to keep the ratio constant is 6.
Here are the completed tables:
TVs 2 4 6
Computers 7 14 21
Trumpets 10 5 20 25
Drums 8 4 16 20
Books 0 40 100
Boxes 0 2 5
What are the ratios?Ratio expresses the relationship between two or more numbers. It is the number of times that one value is contained within other value(s).
The ratio of snakes to frogs can be determined by counting the number of snakes and frogs.
Number of snakes = 4
Number of frogs = 8
The ratio of snakes to frogs - 4 : 8 = 1 : 2
The ratio of frogs to animals = number of frogs : number of animals = 8 : 12 = 2 : 3.
Number of snakes if 3 more are added = 4 + 3 = 7
Ratio of snakes to frogs - 1 : 2
Number of frogs that would keep the ratio constant = 7 x 2 = 14
Number of frogs that should be added = 14 - 8 = 6
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A 2\frac{1}{2}2 2 1 -inch candle burns down in 10 hours. If b represents how much of the candle, in inches, has burned away at any time given in hours, t, write a proportional equation for b in terms of t that matches the context.
The equation that represents the length of the candle over time will be b = -0.25t.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A 2 ¹/₂ inches candle torches in 10 hours.
Let 'b' be the length of the candle and 't' be the number of hours. Then the equation is given as,
b = -[(2 ¹/₂) / (10)]t
b = -0.25t
The equation that represents the length of the candle over time will be b = -0.25t.
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Daniel has invested $300 in an annuity each month, earning 4% interest for 20 years.
Sarah has invested $150 in an annuity each month, earning 4% interest for 40 years.
Which of the following must be true?
Answer: daniel and sarah will deposit the same amount
solve 4x + 2=(1/8)x-2
Answer:
x = -32/31
Step-by-step explanation:
4x - 1/8 x = -2 -2
(32 - 1)/8 x = -4
31/8 x = -4
x = -4 * 8/31
x = -32/31
A house on the market was valued at $355,000 . After several years, the value decreased by 9%. By how much did the house's value decrease in dollars? What is the current value of the house?
Answer: $323,050
Step-by-step explanation:
355,000 over 1 x 9 over 100 = 3195000 over 100 (31950)
355,000- 31,950 = 323,050 which is your answer, hope this helped <3
Suppose a large shipment of stereos contained 18% defectives. If a sample of size 306 is selected, what is the probability that the sample proportion will differ from the population proportion by more than 6%? Round your answer to four decimal places.
The probability that the sample proportion of a large shipment of stereos will differ from the population proportion by more than 6% is 0.0063
How to get the required probabilityThe probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean
The z score is given by the formula
z = (X - μ) / σ
Definition of variables
mean, μ = p = 18% = 0.18
sample size, n = 306
standard deviation, σ
= √{(p(1 - p)) / n}
= √{(0.18(1 - 0.18)) / 306}
= √{(0.18 * 0.82) / 306}
= 0.02196
The probability
differ from the population proportion by less than 3%
|X - 0.18| > 0.06
X < 0.12 OR X > 0.24
P(z < 0.12) + P(z > 0.24 )
z score for z < 0.06
z = (0.12 - 0.18) / 0.02196
= -2.7322
p value for z < -2.7322 = 0.003146
z score for z > 0.06
z = (0.24 - 0.18) / 0.02196
= 2.7322
p value for z > 2.7322 = 1 - 0.99685 = 0.003146
The probability required = 0.003146 + 0.003146 = 0.006292 = 0.63%
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A speed limit in Europe is 80 km per hour. What is the speed in miles per hour? There are about 1.6 kilometers in 1 mile. (1 point)
Responses
50 miles per hour
50 miles per hour
75 miles per hour
75 miles per hour
128 miles per hour
128 miles per hour
50 miles
ned asap
pls answer rightly not spam
Answer:
50 miles per hour
Step-by-step explanation:
80 km 1 mi
---------- x ------------ = 50 mi/hr
1 hr 1.6 km
Fill in the table using this function rule. y=-2x-3
Answer:
6
Step-by-step explanation:
the answer is 6
Which choice is equivalent to the fraction below 2/√x - √x+2
The fraction is equivalent to the [tex]\sqrt{x+2}-\sqrt{x}[/tex].
The correct option is (C).
Given,
The fraction is given as:
[tex]\frac{2}{\sqrt{x} -\sqrt{x+2} }[/tex]
To find the above fraction which choice is equivalent to the fraction?
Now, According to the question:
Simplify or expand
[tex]\frac{2}{\sqrt{x} -\sqrt{x+2} }[/tex]
Rationalize the denominator:
[tex]\frac{2(\sqrt{x} -\sqrt{x+2} )}{(\sqrt{x} -\sqrt{x+2})(\sqrt{x} -\sqrt{x+2} ) }[/tex]
Expand the expression:
[tex]\frac{2(\sqrt{x} +\sqrt{x+2} )}{(\sqrt{x})^2-(\sqrt{x+2} )^2 }[/tex]
[tex]\frac{2(\sqrt{x} +\sqrt{x+2} )}{x-(x+2)}[/tex]
[tex]\frac{2(\sqrt{x} +\sqrt{x+2} )}{-2}[/tex]
Determine the sign and cross out the common factor:
[tex]\sqrt{x+2}-\sqrt{x}[/tex]
Hence, The fraction is equivalent to the [tex]\sqrt{x+2}-\sqrt{x}[/tex].
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Which model represents the sum of 4 + 12?
Answer: 16
Step-by-step explanation:
Imagine you had 4 apples and someone gave you 12 more. You would have 16 apples.
Two year ago ernest dorsey purchased a used sports coupe for 8000.00 that is now worth 6000.00 last year he drove it 13569 miles and kept a record od all expenses. His variable costs were gasoline $1589.56 oil changes $245.98 and repairs $548.11 his fix costs were insurance $1105.32 and license $85 find de cost per mile
The cost per mile incurred by Ernest Dorsey for driving the sports coupe for last year was $0.41.
How is the cost per mile derived?The cost per mile is the quotient of the division operation involving the total cost incurred and the driving mileage for the year.
To derive the total cost, add up the value of the car consumed (cost - current value), the annual variable, and fixed costs.
Cost of a used sports coupe last year = $8,000
The current value of the car = $6,000
Used value for the year = $2,000.00 ($8,000 - $2,000)
Yearly variable costs:Gasoline $1,589.56
Oil changes $245.98
Repairs $548.11 $2,383.65
Annual fixed Costs:Insurance $1,105.32
License $85.00 $1,190.32
Total cost for the year = $5,573.97
Driven mileage for the year = 13,569 miles
Cost per mile = $0.41 ($5,573.97/13,569)
Thus, the cost per mile is $0.41.
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What is the slope of the line on the graph?
Enter your answer in the box.
The diagram shows a triangle. Complete parts a and b below. (4 points)
53⁰
8p+10°
2p+17°
A- write an equation and solve for p. Show all work.
B-List the measures of the three angles.
The value of p is 10 and the angles of the triangles are 53°, 90°, 37°.
Given that,
In the picture there is a triangle with angles 53°, 8p+10°, 2p+17°.
We have to find the p value and each of the angles also.
What is angles in triangles?While the exterior angles of a triangle are equal to the sum of the two interior angles that are not adjacent to it, the interior angles of a triangle always add up to 180°. By deducting the angle of the target vertex from 180°, one can also determine a triangle's exterior angle.
Take the angles ,
180 degrees is the sum of the angles in an triangle.
53°+ 8p+10°+ 2p+17°=180°
10p+80°=180°
10p=180°-80°
10p=100°
p=100/10
p=10°
The value of p=10.
The angles of the triangles are:
53°
8p+10=8(10)+10=80+10=90°
2p+17=2(10)+17=20+17=37°
Therefore, The value of p is 10 and the angles of the triangles are 53°, 90°, 37°.
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Last Friday, Kira and Marcy got dinner at Seaside Sushi restaurant. Kira ordered 2 pieces of tuna and 5 pieces of crab. Marcy ordered 3 pieces of tuna and 6 pieces of crab. Did Kira and Marcy order the same ratio of tuna pieces to crab pieces?
Answer:
no
Step-by-step explanation:
because Kira ordered 5 pieces of crab while Marcy has ordered 6 pieces of crab
is a gas station sells 8 bags of chips for $12, what is the unit price
The ratio shows how many times one value is contained in another value.
8 bags of chips = $12
1 bag of chips = $1.5
The unit price of a bag of chips is $1.5
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
There are 4 black and 3 white marbles in a bag.
The ratio of black and white marbles in the bag is 4:3.
We have,
8 bags of chips = $12
Divide both sides by 8.
1 bag of chips = $12/8
1 bag of chips = $3/2
1 bag of chips = $1.5
This means,
1 bag of chips costs $1.5
Thus,
The unit price of a bag of chips is $1.5
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A car dealership increased the price of a certain car by 13%. The original price was $39,400.
Answer:
find the increased dollar amount by finding the percentage amount first:
$ 39,400 * .13
= $ 5,122
then take $ 5,122 and add it to the original price
$ 39,400 + $ 5,122 = $ 44,522 (new price)
Step-by-step explanation:
Write an equation in slope-intercept form for the line that passes through (3, 1) and (1,2).
The equation of the line that passes through (3, 1) and (1,2) in slope intercept form is y = - 2 / 2 x + 5 / 2.
How to find equation of a line?The equation of a line can be represented in different form such as slope intercept form, point slope form, standard form and general form.
Therefore, let's write the equation of a line that passes through (3, 1) and (1, 2).
using slope intercept form,
y = mx + b
where
m= slopeb = y-interceptTherefore, let's find slope
m = 2 - 1 / 1 - 3
m = 1 / - 2
m = - 1 / 2
Let's find y-intercept using (1, 2)
2 = - 1 / 2(1) + b
b = 2 + 1 / 2
b = 5 / 2
Therefore, the equation is y = - 2 / 2 x + 5 / 2
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